Functions — Quiz 2

Questions in this quiz (10)

1. If $$f(x)=x^3+Cx^2+Dx+5$$ and if $$f(2)=19$$ and $$f(-2)=1,$$ what is the value of $$2C+D$$?

   • $$10$$
   • $$6$$
   • $$3$$
   • $$-4$$

2. Which of the following equations has a graph that is symmetric with respect to the origin?

   • $$y=\frac{x+2}{x}$$
   • $$y=x^4-x^2$$
   • $$y=x^5-3x$$
   • $$y=x^3+4$$

3. Let $$f$$ be a function defined for all real numbers. Which of the following conditions is not sufficient to guarantee that $$f$$ has an inverse function?

   • $$f(x)=mx+c,m\neq0$$
   • $$f$$ is strictly increasing on $$(-\infty,\infty)$$
   • $$f$$ is an even function
   • $$f$$ is one-to-one

4. Let $$y=g(x)=\cos(\arctan x)$$. Then the range of $$g$$ is:

   • $$\{y\mid-1<y<1\}$$
   • $$\{y\mid0<y\le1\}$$
   • $$\{y\mid-\frac{\pi}{2}<y<\frac{\pi}{2}\}$$
   • $$\{y\mid0\le y\le1\}$$

5. Which of the following functions is not odd?

   • $$f(x)=\cos x-\cos(-x)$$
   • $$f(x)=x^{5}$$
   • $$f(x)=x^{3}-2x$$
   • $$f(x)=\frac{x^{2}}{x^{2}+1}$$

6. Let $$h(x)=|\sin x+1|$$. The maximum value attained by $$h$$ on the closed interval $$[0,2\pi]$$ occurs when $$x=$$?

   • $$0$$
   • $$\frac{\pi}{2}$$
   • $$\pi$$
   • $$\frac{3\pi}{2}$$

7. If the solutions to the equation $$g(x)=0$$ are $$x=-3$$ and $$x=4$$, then $$g(3x)=0$$ at which values of $$x$$?

   • $$-9$$ and $$12$$
   • $$-1$$ and $$\frac{4}{3}$$
   • $$-\frac{1}{9}$$ and $$\frac{3}{4}$$
   • $$-\frac{3}{3}$$ and $$\frac{12}{3}$$

8. The set of zeros of $$g(x)=x^3-3x^2-4x$$ is:

   • $$\{-1,4\}$$
   • $$\{0,-1,4\}$$
   • $$\{0,1,-4\}$$
   • $$\{1,4\}$$

9. The values of $$x$$ for which the graphs of $$y=2x-1$$ and $$y^{2}=8x$$ intersect are which of the following?

   • $$-1$$ and $$3$$
   • $$-1$$
   • $$\frac{3\pm2\sqrt{2}}{2}$$
   • No intersection

10. The function whose graph is a reflection in the y axis of the graph of $$f(x)=2+4^{x}$$ is:

    • $$g(x)=2+4^{-x}$$
    • $$g(x)=4^{x}+2$$
    • $$g(x)=\log_{4}(x-2)$$
    • $$g(x)=\log_{4}(2-x)$$